In this paper, we present a conservative finite volume scheme for the gas dynamics in Lagrangian coordinates, which is fast and nondiffusive. By fast, we mean that it relies on an approximate Riemann solver, and hence the costly resolution of Riemann problems is avoided. By nondiffusive, we mean that the solution provided by the scheme is exact when the initial data is an isolated admissible shock, and discontinuities are sharply captured in general. The construction of the scheme uses two main tools: the approximate Riemann solver of [Ch. Chalons and F. Coquel, Math. Models Methods Appl. Sci. 24 (2014) 937–971.], which turns out to be exact on isolated admissible shocks, and a discontinuous reconstruction strategy, which consists in rebuilding entropy satisfying shocks inside some well chosen cells. Numerical experiments in 1D and 2D are proposed.
Accepted:
DOI: 10.1051/m2an/2016010
Mots-clés : Conservative finite volume scheme, discontinuous reconstruction, approximate Riemann solver, non diffusive scheme, Sharp discontinuities
@article{M2AN_2016__50_6_1887_0, author = {Aguillon, Nina and Chalons, Christophe}, title = {Nondiffusive conservative schemes based on approximate {Riemann} solvers for {Lagrangian} gas dynamics}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis }, pages = {1887--1916}, publisher = {EDP-Sciences}, volume = {50}, number = {6}, year = {2016}, doi = {10.1051/m2an/2016010}, zbl = {1388.76163}, mrnumber = {3580126}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an/2016010/} }
TY - JOUR AU - Aguillon, Nina AU - Chalons, Christophe TI - Nondiffusive conservative schemes based on approximate Riemann solvers for Lagrangian gas dynamics JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2016 SP - 1887 EP - 1916 VL - 50 IS - 6 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2016010/ DO - 10.1051/m2an/2016010 LA - en ID - M2AN_2016__50_6_1887_0 ER -
%0 Journal Article %A Aguillon, Nina %A Chalons, Christophe %T Nondiffusive conservative schemes based on approximate Riemann solvers for Lagrangian gas dynamics %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2016 %P 1887-1916 %V 50 %N 6 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2016010/ %R 10.1051/m2an/2016010 %G en %F M2AN_2016__50_6_1887_0
Aguillon, Nina; Chalons, Christophe. Nondiffusive conservative schemes based on approximate Riemann solvers for Lagrangian gas dynamics. ESAIM: Mathematical Modelling and Numerical Analysis , Volume 50 (2016) no. 6, pp. 1887-1916. doi : 10.1051/m2an/2016010. http://www.numdam.org/articles/10.1051/m2an/2016010/
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